Mathematical modeling on peristaltic flow of a Prandtl fluid with effects of slip conditions and inclined magnetic field

Abstract

The manuscript provides a description of a theoretical analysis of a non-Newtonian Prandtl fluid that is subject to peristaltic flow via an inclined asymmetric channel. We explore the effect of an inclined magnetic field on the peristaltic flow. This is relevant for applications of fluid flow in narrow, inclined (tilted) tubes that are similar to blood vessels or to the digestive system. The model also includes thermodynamic aspects such as heat diffusion (the Soret effect) and viscous dissipation as a result of wall–fluid slip conditions, which help optimize medical devices like lab-on-a-chip systems and dialysis machines. In this study, the concentration of a generic chemical, temperature and fluid velocity are taken into account through mass, heat and momentum balances, respectively. The solution is approximated by the use of numerical techniques that are suitable for cases with long wavelengths (low frequency) and low Reynold’s numbers. The study also discusses the effects of trapping phenomena, which is a crucial issue from a clinical point of view. The developed insights can be used to improve the understanding of physiological flows in the gastrointestinal tract and in blood vessels. By understanding how the fluid moves and how particles are trapped, these insights help to design better medical pumps and artificial organs. A graphical visualization is provided for the fluid velocity profile, temperature distribution and concentration of a generic chemical. Furthermore, a validation of our numerical results has been provided by means of a comparison with a closed-form solution from a benchmark problem. The Prandtl fluid parameters $\alpha$ and $\beta$ have an opposite impact on the axial velocity. Furthermore, an increase in the Schmidt number, $Sc$, gives a decrease of the concentration of the dissolved chemical. The model predicts that channel inclination has no significant effect on the concentration profile. Furthermore, the model indicates that the Prandtl fluid parameters $\alpha$ and $\beta$ hardly impact the size of the bolus trapped between the streamlines.